Sauté the butternut squash: In a large pot or Dutch oven, heat 1 tablespoon of butter and 1 tablespoon of olive oil over medium heat. Add the cubed butternut squash and cook, stirring occasionally, for about 10–12 minutes, or until the squash begins to soften and develop light golden edges. This step builds flavor into the final sauce, so don’t rush it.
Simmer with broth and spices: Add the vegetable broth, 1 teaspoon salt, smoked paprika, dried thyme, and dried sage. Stir well, cover the pot with a lid, and reduce the heat to medium-low. Let the squash simmer for 15 minutes, or until completely fork-tender and fragrant.
Cook the pasta: While the squash simmers, bring a large pot of salted water to a boil. Cook the shells or macaroni noodles according to package instructions until al dente. Drain and set aside.
Blend the squash: Once the squash is fully cooked, carefully transfer it (along with any remaining liquid) to a high-powered blender or food processor. Blend until completely smooth and creamy, then set aside. If your mixture is too thick to blend, add a splash of warm broth or milk to help it along.
Make the roux: In the same pot (no need to clean it!), melt the remaining 4 tablespoons of butter over medium heat. Sprinkle in the flour, ½ teaspoon salt, and nutmeg, and stir continuously for 1 minute to form a roux. It should be bubbly and lightly golden, not brown. This will help thicken the cheese sauce.
Add the milk and squash purée: Slowly whisk in the room-temperature milk, stirring constantly to avoid lumps. Turn the heat up to medium and pour in the blended squash. Continue stirring until the mixture is smooth, creamy, and heated through, about 3–5 minutes.
Combine with pasta: Add the cooked pasta to the sauce and stir gently until all the noodles are evenly coated in the creamy squash mixture.
Melt in the cheese: Turn off the heat and fold in the shredded cheddar cheese, a handful at a time, stirring until fully melted and velvety. Taste and adjust with additional salt, if needed.
Garnish and serve: Spoon into bowls and top with fresh thyme leaves or a sprinkle of black pepper, if desired. Serve warm and enjoy!